void smooth_border_vertices( Halfedge_handle e, OutputIterator out) {
CGAL_precondition( e->is_border());
// We know that the vertex at this edge is from the unrefined mesh.
// Get the locus vectors of the unrefined vertices in the neighborhood.
Vector v0 = e->prev()->prev()->opposite()->vertex()->point() -CGAL::ORIGIN;
Vector v1 = e->vertex()->point() - CGAL::ORIGIN;
Vector v2 = e->next()->next()->next()->vertex()->point() - CGAL::ORIGIN;
*out++ = CGAL::ORIGIN + (10.0 * v0 + 16.0 * v1 + v2) / 27.0;
*out++ = CGAL::ORIGIN + ( 4.0 * v0 + 19.0 * v1 + 4.0 * v2) / 27.0;
*out++ = CGAL::ORIGIN + ( v0 + 16.0 * v1 + 10.0 * v2) / 27.0;
}
void trisect_border_halfedge( Polyhedron& P, Halfedge_handle e) {
CGAL_precondition( e->is_border());
// Create two new vertices on e.
e = e->prev();
P.split_vertex( e, e->next()->opposite());
P.split_vertex( e, e->next()->opposite());
e = e->next();
// We use later for the smoothing step that e->next()->next()
// is our original halfedge we started with, i.e., its vertex is
// from the unrefined mesh. Split the face twice.
Halfedge_handle h = e->opposite()->next();
P.split_facet( e->next()->next()->opposite(), h);
P.split_facet( e->next()->opposite(), h);
}